A neutral network is a set of

gene In biology, the word gene has two meanings. The Mendelian gene is a basic unit of heredity. The molecular gene is a sequence of nucleotides in DNA that is transcribed to produce a functional RNA. There are two types of molecular genes: protei ...

s all related by

point mutation A point mutation is a genetic mutation where a single nucleotide base is changed, inserted or deleted from a DNA or RNA sequence of an organism's genome. Point mutations have a variety of effects on the downstream protein product—consequences ...

s that have equivalent function or fitness. Each node represents a gene sequence and each line represents the mutation connecting two sequences. Neutral networks can be thought of as high, flat plateaus in a

fitness landscape Fitness may refer to: * Physical fitness, a state of health and well-being of the body * Fitness culture, a sociocultural phenomenon surrounding exercise and physical fitness * Fitness (biology), an individual's ability to propagate its genes * ...

. During

neutral evolution The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift of mutant alleles that are selectively neutral. The ...

, genes can randomly move through neutral networks and traverse regions of

sequence space In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural num ...

which may have consequences for

robustness Robustness is the property of being strong and healthy in constitution. When it is transposed into a system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, ...

and

evolvability Evolvability is defined as the capacity of a system for adaptive evolution. Evolvability is the ability of a population of organisms to not merely generate genetic diversity, but to generate '' adaptive'' genetic diversity, and thereby evolve thr ...

Genetic and molecular causes

Neutral networks exist in

s since proteins are

robust Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system's functional body. In the same line ''robustness'' can ...

to mutations. This leads to extended networks of genes of equivalent function, linked by

neutral mutation Neutral mutations are changes in DNA sequence that are neither beneficial nor detrimental to the ability of an organism to survive and reproduce. In population genetics, mutations in which natural selection does not affect the spread of the mutatio ...

s. Proteins are resistant to mutations because many sequences can fold into highly similar structural folds. A protein adopts a limited ensemble of native conformations because those conformers have lower energy than unfolded and mis-folded states (ΔΔG of folding). This is achieved by a distributed, internal network of cooperative interactions (

hydrophobic In chemistry, hydrophobicity is the chemical property of a molecule (called a hydrophobe) that is seemingly repelled from a mass of water. In contrast, hydrophiles are attracted to water. Hydrophobic molecules tend to be nonpolar and, thu ...

polar Polar may refer to: Geography * Geographical pole, either of the two points on Earth where its axis of rotation intersects its surface ** Polar climate, the climate common in polar regions ** Polar regions of Earth, locations within the polar circ ...

and

covalent A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...

). Protein structural robustness results from few single mutations being sufficiently disruptive to compromise function. Proteins have also evolved to avoid aggregation as partially folded proteins can combine to form large, repeating, insoluble protein fibrils and masses. There is evidence that proteins show negative design features to reduce the exposure of aggregation-prone

beta-sheet The beta sheet (β-sheet, also β-pleated sheet) is a common structural motif, motif of the regular protein secondary structure. Beta sheets consist of beta strands (β-strands) connected laterally by at least two or three backbone chain, backbon ...

motifs in their structures. Additionally, there is some evidence that the

genetic code Genetic code is a set of rules used by living cell (biology), cells to Translation (biology), translate information encoded within genetic material (DNA or RNA sequences of nucleotide triplets or codons) into proteins. Translation is accomplished ...

itself may be optimised such that most point mutations lead to similar amino acids (

conservative Conservatism is a cultural, social, and political philosophy and ideology that seeks to promote and preserve traditional institutions, customs, and values. The central tenets of conservatism may vary in relation to the culture and civiliza ...

). Together these factors create a

distribution of fitness effects In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA replication, DNA or viral rep ...

of mutations that contains a high proportion of neutral and nearly-neutral mutations.

Evolution

Neutral networks are a subset of the sequences in

that have equivalent function, and so form a wide, flat

plateau In geology and physical geography, a plateau (; ; : plateaus or plateaux), also called a high plain or a tableland, is an area of a highland consisting of flat terrain that is raised sharply above the surrounding area on at least one side. ...

in a

Neutral evolution The neutral theory of molecular evolution holds that most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift of mutant alleles that are selectively neutral. The ...

can therefore be visualised as a population diffusing from one set of sequence nodes, through the neutral network, to another cluster of sequence nodes. Since the majority of evolution is thought to be neutral,Kimura, Motoo. (1983). ''The neutral theory of molecular evolution.'' Cambridge a large proportion of gene change is the movement though expansive neutral networks.

Robustness

The more neutral neighbours a sequence has, the more robust to mutations it is since mutations are more likely to simply neutrally convert it into an equally functional sequence. Indeed, if there are large differences between the number of neutral neighbours of different sequences within a neutral network, the population is predicted to evolve towards these robust sequences. This is sometimes called circum-neutrality and represents the movement of populations away from cliffs in the

. In addition to in silico models, these processes are beginning to be confirmed by

experimental evolution Experimental evolution is the use of laboratory experiments or controlled field manipulations to explore evolutionary dynamics. Evolution may be observed in the laboratory as populations adapt to new environmental conditions by natural selection. ...

cytochrome P450 Cytochromes P450 (P450s or CYPs) are a Protein superfamily, superfamily of enzymes containing heme as a cofactor (biochemistry), cofactor that mostly, but not exclusively, function as monooxygenases. However, they are not omnipresent; for examp ...

s and B-lactamase.

Evolvability

Interest in the interplay between

genetic drift Genetic drift, also known as random genetic drift, allelic drift or the Wright effect, is the change in the Allele frequency, frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene va ...

and selection has been around since the 1930s when the shifting-balance theory proposed that in some situations, genetic drift could facilitate later adaptive evolution. Although the specifics of the theory were largely discredited, it drew attention to the possibility that drift could generate cryptic variation that, though neutral to current function, may affect selection for new functions (

). By definition, all genes in a neutral network have equivalent function, however some may exhibit promiscuous activities which could serve as starting points for adaptive evolution towards new functions. In terms of

, current theories predict that if the neutral networks for two different activities overlap, a neutrally evolving population may diffuse to regions of the neutral network of the first activity that allow it to access the second. This would only be the case when the distance between activities is smaller than the distance that a neutrally evolving population can cover. The degree of interpenetration of the two networks will determine how common cryptic variation for the promiscuous activity is in sequence space.

Mathematical Framework

The fact that neutral mutations were probably widespread was proposed by Freese and Yoshida in 1965.

Motoo Kimura (November 13, 1924 – November 13, 1994) was a Japanese biologist best known for introducing the neutral theory of molecular evolution in 1968. He became one of the most influential theoretical population geneticists. He is remembered in ge ...

later crystallized a theory of neutral evolution in 1968 with King and Jukes independently proposing a similar theory (1969). Kimura computed the rate of nucleotide substitutions in a population (i.e. the average time for one base pair replacement to occur within a genome) and found it to be ~1.8 years. Such a high rate would not be tolerated by any mammalian population according to Haldane's formula. He thus concluded that, in mammals, neutral (or nearly neutral) nucleotide substitution mutations of

DNA Deoxyribonucleic acid (; DNA) is a polymer composed of two polynucleotide chains that coil around each other to form a double helix. The polymer carries genetic instructions for the development, functioning, growth and reproduction of al ...

must dominate. He computed that such mutations were occurring at the rate of roughly 0-5 per year per gamete. SimpleGenotypePhenotypeMap

In later years, a new paradigm emerged, that placed

RNA Ribonucleic acid (RNA) is a polymeric molecule that is essential for most biological functions, either by performing the function itself (non-coding RNA) or by forming a template for the production of proteins (messenger RNA). RNA and deoxyrib ...

as a precursor molecule to

. A primordial molecule principle was put forth as early as 1968 by Crick, and lead to what is now known as The RNA World Hypothesis.

is found, predominantly, as fully

base pair A base pair (bp) is a fundamental unit of double-stranded nucleic acids consisting of two nucleobases bound to each other by hydrogen bonds. They form the building blocks of the DNA double helix and contribute to the folded structure of both DNA ...

ed double helices, while biological

is single stranded and often exhibits complex base-pairing interactions. These are due to its increased ability to form

hydrogen bond In chemistry, a hydrogen bond (H-bond) is a specific type of molecular interaction that exhibits partial covalent character and cannot be described as a purely electrostatic force. It occurs when a hydrogen (H) atom, Covalent bond, covalently b ...

s, a fact which stems from the existence of the extra

hydroxyl In chemistry, a hydroxy or hydroxyl group is a functional group with the chemical formula and composed of one oxygen atom covalently bonded to one hydrogen atom. In organic chemistry, alcohols and carboxylic acids contain one or more hydroxy ...

group in the

ribose Ribose is a simple sugar and carbohydrate with molecular formula C5H10O5 and the linear-form composition H−(C=O)−(CHOH)4−H. The naturally occurring form, , is a component of the ribonucleotides from which RNA is built, and so this comp ...

sugar. In the 1970s, Stein and M. Waterman laid the groundwork for the combinatorics of

secondary structures. Waterman gave the first graph theoretic description of

secondary structures and their associated properties, and used them to produce an efficient minimum free energy (MFE) folding algorithm. An

secondary structure can be viewed as a diagram over N labeled vertices with its Watson-Crick

s represented as non-crossing arcs in the upper half plane. Therefore, a

secondary structure Protein secondary structure is the local spatial conformation of the polypeptide backbone excluding the side chains. The two most common Protein structure#Secondary structure, secondary structural elements are alpha helix, alpha helices and beta ...

is a scaffold having many sequences compatible with its implied base pairing constraints. Later, Smith and Waterman developed an algorithm that performed local sequence alignment. Another prediction algorithm for

secondary structure was given by Nussinov Nussinov's algorithm described the folding problem over a two letter alphabet as a planar graph optimization problem, where the quantity to be maximized is the number of matchings in the sequence string. Come the year 1980, Howell et al. computed a generating function of all foldings of a sequence while D. Sankoff (1985) described algorithms for alignment of finite sequences, the prediction of RNA secondary structures (folding), and the reconstruction of proto-sequences on a phylo-genetic tree. Later, Waterman and

Temple A temple (from the Latin ) is a place of worship, a building used for spiritual rituals and activities such as prayer and sacrifice. By convention, the specially built places of worship of some religions are commonly called "temples" in Engli ...

(1986) produced a

polynomial time In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations p ...

dynamic programming (DP) algorithm for predicting general

secondary structure. while in the year 1990, John McCaskill presented a polynomial time DP algorithm for computing the full equilibrium partition function of an RNA secondary structure. This changed the dominant calculation of RNA folding from a mapping of sequence to a particular 3D structure, to a mapping of sequence to a whole weighted ensemble of structures, which smooths RNA fitness, which depends on sequence via folding, facilitating more nearly neutral nets. M. Zuker, implemented algorithms for computation of MFE

secondary structures based on the work of Nussinov et al., Smith and Waterman and Studnicka, et al. Later L. Hofacker (et al., 1994), presented The Vienna RNA package, a software package that integrated MFE folding and the computation of the partition function as well as base pairing probabilities.

Peter Schuster Peter K. Schuster (born 7 March 1941) is a theoretical chemist known for his work with the German Nobel Laureate Manfred Eigen in developing the quasispecies model. His work has made great strides in the understanding of viruses and their repl ...

and W. Fontana (1994) shifted the focus towards sequence to structure maps ( genotype–phenotype) . They used an inverse folding algorithm, to produce computational evidence that

sequences sharing the same structure are distributed randomly in

. They observed that common structures can be reached from a random sequence by just a few mutations. These two facts lead them to conclude that the sequence space seemed to be percolated by neutral networks of nearest neighbor mutants that fold to the same structure. In 1997, C. Reidys Stadler and

Schuster Schuster ("shoemaker", "cobbler") is a common family name in German. It is also common among Ashkenazi Jews, sometimes spelled Shuster. Other spelling variants of the name include Šuster, Šustr, Šuštar, and Chouster. People * Alfredo Ildef ...

laid the mathematical foundations for the study and modelling of neutral networks of

secondary structures. Using a random graph model they proved the existence of a threshold value for connectivity of random sub-graphs in a configuration space, parametrized by λ, the fraction of neutral neighbors. They showed that the networks are connected and

percolate In physics, chemistry, and materials science, percolation () refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applications have since been developed that cover connectivity of man ...

sequence space if the fraction of neutral nearest neighbors exceeds λ*, a threshold value. Below this threshold the networks are partitioned into a largest

giant component In network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices. More precisely, in graphs drawn randomly from a probability distribution over arbitrarily ...

and several smaller ones. Key results of this analysis where concerned with threshold functions for density and connectivity for neutral networks as well as

's shape space conjecture.

References